The Art of Sudoku: Solving Seven by Seven Magic Squares

A Seven by Seven magic square is a two-dimensional grid of numbers where the sum of each row, column, and diagonal is the same. In this case, the sum is the magic constant, which is calculated by multiplying the number of rows (seven) by the sum of the numbers from 1 to seven, and then dividing by two. The main idea of the Seven by Seven magic square is that it is a unique arrangement of numbers that satisfies the condition of having the same sum in each row, column, and diagonal. It is a mathematical construct that has been studied for centuries and holds significance in various fields such as mathematics, puzzles, and recreational mathematics. Creating a Seven by Seven magic square involves placing the numbers from 1 to 49 in a specific arrangement. The first number is usually placed in the middle column of the top row, and subsequent numbers are placed diagonally upwards and to the right.

This square adds up to 62 in 13 ways.

You could start with the number 1 anywhere, but if you put it in the middle of the top line, this ensures that the diagonals work and that the 4 corners and the middle number add up to 65. Viz - Generating and Counting Magic Squares Taudevin For those who would like to see some results from Glen Duff s Square generating programme, below are illustrated various types of square with their metrics.

The first number is usually placed in the middle column of the top row, and subsequent numbers are placed diagonally upwards and to the right. If a number goes beyond the bounds of the square, it wraps around to the opposite side. The Seven by Seven magic square is also symmetric, meaning that it can be rotated or flipped without changing the sum of each row, column, and diagonal.

How to make bigger Magic Squares

How to make a 5x5 magic square add up to other numbers.

This square adds up to 62 in 13 ways.

You'll see it's very similar to the first square but we've subtracted 3 from each number in a red box. That's why each line adds up to 3 less than 65.

If you wanted each line to add up to 80, that's 15 more than 65. So starting with the original square, you'd just add 15 to each number in a red square. However, we can do better than that!

How to lay out a 5x5 Magic Square

Have another look at the way the numbers are set out in the original square. It uses all the numbers 1-25, and if you follow the numbers round in order you'll see they appear in this pattern:

1,2,3,4 and 5 are in a diagonal line, which goes off the top and comes back at the bottom, then goes off the right and comes back on the left. Once the first five numbers are in place, there's no empty place to put number 6.

Again you'll see that the numbers 6-10 are in a diagonal which goes round until there's no space for the 11. So the 11 goes under the last number which was 10. If you keep going, you'll fill the whole grid with the numbers 1-25 and make the basic 5x5 magic square.

** You could start with the number 1 anywhere, but if you put it in the middle of the top line, this ensures that the diagonals work and that the 4 corners and the middle number add up to 65.**

So suppose you want the square to add to 80?

Instead of starting with the number 1, start with a 4, then continue filling in 5,6,7,8 etc. until you finish on 28.

You get a square like this one:

• Take the lowest number and multiply by 5.
• Add 60

In this case it's 4 x 5 + 60 = 20 + 60 = 80

7x7 Magic Squares

A 7x7 square works the same way as a 5x5 square - just fill in the numbers in diagonals as before. Sadly the four corners and middle number don't give the right result, but you'll find all the lines and diagonals add up to 175!

The "KNIGHT'S MOVE" 8x8 Magic Square

If you know the rules of chess, you'll know that it's played on a board measuring 8 squares by 8 squares. One chess piece is the "knight" and it moves around the board in a strange way. It leaps around in a little "L" shape - in other words it goes two steps forward and one step to the side. In this little diagram, if the "knight" was on the yellow square in the middle, then the red squares show where it could jump to.

The classic "Knight's Puzzle" is to try and move a knight round a chess board visiting every square just once. It's a tough puzzle at the best of times, but here is one very special solution! The knight starts on the square numbered 1 then hops to 2, then 3 etc. finally finishing on 64. (It could then hop back to 1 and start again!)

Here's the good bit - every row and every column add up to 260!

The "UPSIDE DOWN" Magic Square

Finally look at this peculiar 4x4 magic square.

Every row and column and both diagonals add up to 19,998 - but if you turn your computer screen upside down it still works!

There's a reasonably simple explanation for this. Can you see it?

When all of the possible combinations are used for all six Graeco-Latin squares, a total of four duplicates of every square are produced.

This symmetry adds to its aesthetic appeal and makes it aesthetically pleasing to the eye. The Seven by Seven magic square can also be used as a basis for creating larger magic squares. By extending the pattern and applying the same rules, it is possible to create larger magic squares with the same properties as the original Seven by Seven square. Overall, the Seven by Seven magic square is a fascinating mathematical concept that showcases the beauty of numbers and their patterns. It is a unique arrangement of numbers that has captivated mathematicians and puzzle enthusiasts for centuries..

Reviews for "The Intricate Patterns of Seven by Seven Magic Squares"

1. Jack - 1/5

I found the "Seven by seven magic square" to be extremely confusing and difficult to follow. The instructions were not clear, and I struggled to create a square that followed the given rules. Additionally, the concept of a magic square itself was not appealing to me, and I didn't find any enjoyment in trying to solve it. Overall, I was disappointed with this puzzle and would not recommend it to others.

2. Sarah - 2/5

While I appreciate the effort put into creating the "Seven by seven magic square," I personally did not find it engaging or enjoyable. The instructions provided were not easy to understand, and I found myself constantly referring back to them to make sure I was following the rules correctly. The puzzle itself was challenging, but not in a way that I found stimulating or satisfying. I felt frustrated and gave up halfway through. Maybe it would be more suitable for someone who has a greater interest in magic squares, but it simply wasn't for me.

3. Emily - 2/5

As someone who enjoys logic puzzles and brain teasers, I was excited to try the "Seven by seven magic square." However, I was disappointed by how convoluted and confusing the instructions were. It was not clear how to approach the puzzle or what the end goal was. This made the solving process frustrating and unsatisfying. Additionally, I found the size of the square to be overwhelming, as it involved too many numbers and variables to keep track of. Overall, I did not find this puzzle to be enjoyable or rewarding.

4. Michael - 2/5

I struggled to find any enjoyment in the "Seven by seven magic square." The concept and rules of the puzzle were difficult to understand, which made it hard for me to even attempt to solve it. The lack of clear instructions and guidance made the whole experience frustrating. I wish there had been more explanations and examples provided to make it more accessible to beginners like myself. I ended up giving up and feeling dissatisfied with the entire puzzle.

A Journey into the World of Seven by Seven Magic Squares